Reduce to lowest terms: $ \dfrac{9}{7} \div - \dfrac{3}{4} = {?}$
Answer: Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $- \dfrac{3}{4}$ is $- \dfrac{4}{3}$ Therefore: $ \dfrac{9}{7} \div - \dfrac{3}{4} = \dfrac{9}{7} \times - \dfrac{4}{3} $ $ \phantom{ \dfrac{9}{7} \times - \dfrac{4}{3}} = \dfrac{9 \times -4}{7 \times 3} $ $ \phantom{ \dfrac{9}{7} \times - \dfrac{4}{3}} = \dfrac{-36}{21} $ The numerator and denominator have a common divisor of $3$, so we can simplify: $ \dfrac{-36}{21} = \dfrac{-36 \div 3}{21 \div 3} = -\dfrac{12}{7} $